What is ln((x^2)/(sqrt(x^2+1)))-1/x-arctan(x)+c ?

The solution to ln((x^2)/(sqrt(x^2+1)))-1/x-arctan(x)+c is 2ln(x)-ln(sqrt(x^2+1))-1/x-arctan(x)+c

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simplify ln((x^2)/(sqrt(x^2+1)))-1/x-arctan(x)+c

simplify

ln (\frac{x ^{2}}{x ^{2} + 1}) - \frac{1}{x} - arctan (x) + c

2 ln (x) - ln (x^{2} + 1) - \frac{1}{x} - arctan (x) + c

Solution steps

ln (\frac{x ^{2}}{x ^{2} + 1}) - \frac{1}{x} - arctan (x) + c

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{x ^{2}}{x ^{2} + 1}) = ln (x^{2}) - ln (x^{2} + 1)

= ln (x^{2}) - ln (x^{2} + 1) - \frac{1}{x} - arctan (x) + c

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{2}) = 2 ln (x)

= 2 ln (x) - ln (x^{2} + 1) - \frac{1}{x} - arctan (x) + c

1 - ln (\frac{3}{2})

ln (\frac{ln ( 2 )}{4})

ln (y^{5} x^{6})

- lo g_{10} (1.64 \cdot 1 0^{- 2})

ln (x + 5) + ln (2)

What is ln((x^2)/(sqrt(x^2+1)))-1/x-arctan(x)+c ?
The solution to ln((x^2)/(sqrt(x^2+1)))-1/x-arctan(x)+c is 2ln(x)-ln(sqrt(x^2+1))-1/x-arctan(x)+c